Maximum Penalized Likelihood Estimation

Volume II: Regression

AvPaul P. Eggermont,Vincent N. LaRiccia

Inbunden, Engelska, 2009

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Beskrivning

This book is intended for graduate students in statistics and industrial mathematics, as well as researchers and practitioners in the field. We cover both theory and practice of nonparametric estimation. The text is novel in its use of maximum penalized likelihood estimation, and the theory of convex minimization problems (fully developed in the text) to obtain convergence rates. We also use (and develop from an elementary view point) discrete parameter submartingales and exponential inequalities. A substantial effort has been made to discuss computational details, and to include simulation studies and analyses of some classical data sets using fully automatic (data driven) procedures. Some theoretical topics that appear in textbook form for the first time are definitive treatments of I.J. Good's roughness penalization, monotone and unimodal density estimation, asymptotic optimality of generalized cross validation for spline smoothing and analogous methods for ill-posed least squares problems, and convergence proofs of EM algorithms for random sampling problems.

Produktinformation

Utgivningsdatum:2009-07-06
Mått:155 x 235 x 41 mm
Vikt:992 g
Format:Inbunden
Språk:Engelska
Serie:Springer Series in Statistics
Antal sidor:572
Upplaga:2009
Förlag:Springer-Verlag New York Inc.
ISBN:9780387402673

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Mikroekonomi inom Ekonomi och Ledarskap
Systemvetenskap och AI inom Data och IT
Matematisk statistik inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "This book is meant for specialized readers or graduate students interested in the theory, computation and application of Nonparametric Regression to real data, and the new contributions of the authors. ... For mathematically mature readers, the book would be a delight to read. ... The authors have not only written a scholarly and very readable book but provide major new methods and insights. ... it would help evaluate the methods as well as lead to teachable notes for a graduate course." (Jayanta K. Ghosh, International Statistical Review, Vol. 79 (1), 2011) "This book is the second volume of a three-volume textbook in the Springer Series in Statistics. ... The second volume also belongs to the literature on nonparametric statistical inference and concentrates mainly on nonparametric regression. ... The book can be used for two main purposes: as a textbook for M.S./Ph.D. students in statistics, operations research, and applied mathematics, and as a tool for researchers and practitioners in these fields who want to develop and to apply nonparametric regression methods." (Yurij S. Kharin, Mathematical Reviews, Issue 2012 g)

Innehållsförteckning

Nonparametric Regression.- Smoothing Splines.- Kernel Estimators.- Sieves.- Local Polynomial Estimators.- Other Nonparametric Regression Problems.- Smoothing Parameter Selection.- Computing Nonparametric Estimators.- Kalman Filtering for Spline Smoothing.- Equivalent Kernels for Smoothing Splines.- Strong Approximation and Confidence Bands.- Nonparametric Regression in Action.